Part IV: Sections 5.5 - 5.717.Suppose that the number of defects in a randomly selectedone carat dliamond of a certain type follows a Poisson distribution withX= 3.By the Central Limit Theorem, what is the approximate(a)distribution of the mean number of defects in the random sample of 40one carat diamonds? You should give a name for the distribution, as welltwo associated numerical quantities.Estimate the largest number of defects y such that in(b)the random sample of 40 one carat diamonds, the probability that thesample mean number of defects is less than y is less than 98%.

Number of defects in one carat diamond follows a Poisson distribution with mean 3. So, mean number…

Answered: Part IV: Sections 5.5 - 5.7 17. Suppose…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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5. On an examination the average grade was 74 and the standard deviation was 7. If 12% of the class are given A's, and the grades are curved to follow normal distribution, what is the lowest possible A and the highest possible B? P(Z < = 1-0.12 = 0.88 1o nou X1 - 74 X1 = 7
Suppose x has a distribution with a mean of 50 and a standard deviation of 36. Random samples of size n = 64 are drawn.
Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer). Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.6 (suggested by the article "Computation Time of Grid Computing with Data Transfer Times that Follow a Gamma Distribution,"+). (a) What are the values of a and ß? (Round your answers to four decimal places.) α = ß = (b) What is the probability that data transfer time exceeds 48 ms? (Round your answer to three decimal places.) (c) What is the probability that data transfer time is between 48 and 72 ms? (Round your answer to three decimal places.)
5. The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimcters. Assume the distributions of both types of breeds are normally distributed. (n) Suppose we are taking a random sample of 64 terriers. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 61 terriers excoedls 75 centimetcrs. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers excoeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.
Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Suppose that the mean and standard deviation for a population of individuals are 180 mg/dl and 20 mg/dl, respectively. Samples are obtained from 25 individuals, and these are independent. (a) What is the probability that the average of the 25 measurements exceeds 185 mg/dl? (b) Determine symmetric limits around 180 such that the probability that the sample average is within the limits equals 0.95.
Let X denote the data transfer time (ms) in a grid computing system (the time required for data transfer between a "worker" computer and a "master" computer). Suppose that X has a gamma distribution with mean value 37.5 ms and standard deviation 21.6 (suggested by the article "Computation Time of Grid Computing with Data Transfer Times that Follow a Gamma Distribution, "t). (a) What are the values of a and 8? (Round your answers to four decimal places.) a = 3.0141 B = 12.4416 (b) what is the probability that data transfer time exceeds 51 ms? (Round your answer to three decimal places.) 0.265 (c) What is the probability that data transfer time is between 51 and 79 ms? (Round your answer to three decimal places.) 0.210 You may need to use the appropriate table in the Appendix of Tables to answer this question.

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